The Role of Feedback Loops in Dynamical Symptom Networks

Motivation

“Once depression or anxiety hits, a feedback loop from hell can begin. We start to feel depressed about being depressed, anxious about feeling anxious. Fighting a negative experience is a negative experience in itself. To prevent this feedback loop, we should accept our pain, not fight it.” — Mark Manson, The Subtle Art of Not Giving a F*ck

Motivation (cont.)

As with most systemic conditions, feedback loops are likely to play a key role in explaining the observed patterns of depression. (Wittenborn et al. 2016)

Mental disorder is produced by direct causal interactions between symptoms that reinforce each other via feedback loops. (Borsboom and Cramer 2013).

Toy model

Adjacency matrix (for the weighted directed graph) determined based on insights from some empirical studies (Ramos-Vera, Banos-Chaparro, and Ogundokun 2021; Lee et al. 2023; Jing et al. 2023).

Model equation \[\begin{equation} dS_{i} = S_{i}(1-S_{i})\left(\beta_i + \alpha_{ii} S_{i} + \sum_{\substack{j=1\\j \neq i}}^9\alpha_{ji}S_{j}(1+\delta_iS_{i}^{2})\right) dt + \sigma_i dW_{i} , i=1, 2, \dots, 9. \end{equation}\]

Description of parameters

Parameter	Description
\(\beta_i\)	The sensitivity level of \(S_i\) to external triggering factors.
\(\alpha\)	The elements of the weight matrix \(\mathbf{A}\). \(\alpha_{ij}\) refers to the weight of the edge \(S_i \rightarrow S_j\) and \(\alpha_{ii}\) refers to the weight of the self-reinforcing loop of \(S_i\).
\(\delta_i\)	The boosting factor that amplifies the effect of other \(S_j\)’s on \(S_i\).
\(\sigma_i\)	The scaling factor that controls the strength of the stochastic term.

Simulation steps

flowchart TD
        A(1. Set reference model) --> B(2. Generate synthetic networks)
        B --> C(3. Extract topological features)
        C --> D(4. Simulate symptom dynamics)

    %% Apply different colors to each node
    style A fill:#F4B9AD,stroke:#333,stroke-width:2px;
    style B fill:#CADBF9,stroke:#333,stroke-width:2px;  
    style C fill:#CADBF9,stroke:#333,stroke-width:2px;  
    style D fill:#CADBF9,stroke:#333,stroke-width:2px;  

    %% Apply different colors to arrows

Our reference model:

Simulation steps

flowchart TD
        A(1. Set reference model) --> B(2. Generate synthetic networks)
        B --> C(3. Extract topological features)
        C --> D(4. Simulate symptom dynamics)

    %% Apply different colors to each node
    style A fill:#CADBF9,stroke:#333,stroke-width:2px;
    style B fill:#F4B9AD,stroke:#333,stroke-width:2px;  
    style C fill:#CADBF9,stroke:#333,stroke-width:2px;  
    style D fill:#CADBF9,stroke:#333,stroke-width:2px;

Our reference model:

The total number of possible network configurations is \(2^n\), where \(n\) is the number of independent edges.
There are 17 edges — two are dependent: a feedback loop between sad and guilt).
The feedback loop itself can have 3 distinct configurations.
The total number of unique network configurations derivable from our example network is \(2^{15} \times 3 =\) 98,304.

Given the reference network structure, we explore all possible network configurations by systematically altering the directions of edges. The total number of possible network configurations is \(2^n\), where \(n\) is the number of independent edges.

In our example, there are 17 edges, but 2 are dependent due to a feedback loop between sad and guilt. This reduces the number of independent edges to 15.

The feedback loop itself can have 3 distinct configurations: (1) both edges in their original direction, maintaining the loop, (2) one edge flipped while the other remains unchanged, causing both edges to point in the same direction, or (3) the other edge flipped, reversing the direction. Instead of the 4 possible combinations (\(2^2\)), this loop yields only 3 unique configurations.

The remaining 15 independent edges can produce \(2^{15}\) possible configurations. Combining these with the 3 unique configurations of the feedback loop, the total number of unique network configurations derivable from our example network is \(2^{15} \times 3 =\) 98,304.

Simulation steps

flowchart TD
        A(1. Set reference model) --> B(2. Generate synthetic networks)
        B --> C(3. Extract topological features)
        C --> D(4. Simulate symptom dynamics)

    %% Apply different colors to each node
    style A fill:#CADBF9,stroke:#333,stroke-width:2px;
    style B fill:#CADBF9,stroke:#333,stroke-width:2px;  
    style C fill:#F4B9AD,stroke:#333,stroke-width:2px;  
    style D fill:#CADBF9,stroke:#333,stroke-width:2px;  

    %% Apply different colors to arrows

topological features

Simulation steps

flowchart TD
        A(1. Set reference model) --> B(2. Generate synthetic networks)
        B --> C(3. Extract topological features)
        C --> D(4. Simulate symptom dynamics)

    %% Apply different colors to each node
    style A fill:#CADBF9,stroke:#333,stroke-width:2px;
    style B fill:#CADBF9,stroke:#333,stroke-width:2px;  
    style C fill:#CADBF9,stroke:#333,stroke-width:2px;  
    style D fill:#F4B9AD,stroke:#333,stroke-width:2px;  

    %% Apply different colors to arrows

Simulate dynamics

Results

Currently..

Thank you

Comments / Questions?
Contact: k.park@uva.nl

Vítor Vasconcelos Vítor V. Vasconcelos Mike Lees

References

Borsboom, Denny, and Angélique OJ Cramer. 2013. “Network Analysis: An Integrative Approach to the Structure of Psychopathology.” Annual Review of Clinical Psychology 9 (1): 91–121.

Jing, Zhi, Fengqin Ding, Yishu Sun, Sensen Zhang, and Ning Li. 2023. “Comparing Depression Prevalence and Associated Symptoms with Intolerance of Uncertainty Among Chinese Urban and Rural Adolescents: A Network Analysis.” Behavioral Sciences 13 (8): 662. https://doi.org/10.3390/bs13080662.

Lee, Eun-Hyun, Eun Hee Kang, Hyun-Jung Kang, and Hyun Young Lee. 2023. “Measurement Invariance of the Patient Health Questionnaire-9 Depression Scale in a Nationally Representative Population-Based Sample.” Frontiers in Psychology 14. https://www.frontiersin.org/articles/10.3389/fpsyg.2023.1217038.

Ramos-Vera, Cristian, Jonatan Banos-Chaparro, and Roseline Oluwaseun Ogundokun. 2021. “The Network Structure of Depressive Symptomatology in Peruvian Adults with Arterial Hypertension.” 10:19. F1000Research. https://doi.org/10.12688/f1000research.27422.2.

Wittenborn, AK, H Rahmandad, J Rick, and N Hosseinichimeh. 2016. “Depression as a Systemic Syndrome: Mapping the Feedback Loops of Major Depressive Disorder.” Psychological Medicine 46 (3): 551–62.